Alpha-Beta-Zero to dq0, dq0 to Alpha-Beta-Zero
Perform transformation from αβ0 stationary reference frame to dq0 rotating reference frame or the inverse
Library
Simscape / Electrical / Specialized Power Systems / Control
Description
The Alpha-Beta-Zero to dq0 block performs a transformation of αβ0 Clarke components in a fixed reference frame to dq0 Park components in a rotating reference frame.
The dq0 to Alpha-Beta-Zero block performs a transformation of dq0 Park components in a rotating reference frame to αβ0 Clarke components in a fixed reference frame.
The block supports the two conventions used in the literature for Park transformation:
Rotating frame aligned with A axis at t = 0. This type of Park transformation is also known as the cosine-based Park transformation.
Rotating frame aligned 90 degrees behind A axis. This type of Park transformation is also known as the sine-based Park transformation. Use it in Simscape™ Electrical™ Specialized Power Systems models of three-phase synchronous and asynchronous machines.
Knowing that the position of the rotating frame is given by ω.t (where ω represents the frame rotation speed), the αβ0 to dq0 transformation performs a −(ω.t) rotation on the space vector Us = uα + j· uβ. The homopolar or zero-sequence component remains unchanged.
Depending on the frame alignment at t = 0, the dq0 components are deduced from αβ0 components as follows:
When the rotating frame is aligned with A axis, the following relations are obtained:
The inverse transformation is given by
When the rotating frame is aligned 90 degrees behind A axis, the following relations are obtained:
The inverse transformation is given by
The abc-to-Alpha-Beta-Zero transformation applied to a set of balanced three-phase sinusoidal quantities ua, ub, uc produces a space vector Us whose uα and uβ coordinates in a fixed reference frame vary sinusoidally with time. In contrast, the abc-to-dq0 transformation (Park transformation) applied to a set of balanced three-phase sinusoidal quantities ua, ub, uc produces a space vector Us whose ud and uq coordinates in a dq rotating reference frame stay constant.
Parameters
- Rotating frame alignment (at wt=0)
Select the alignment of rotating frame, when wt = 0, of the dq0 components of a three-phase balanced signal:
(positive-sequence magnitude = 1.0 pu; phase angle = 0 degree)
When you select
Aligned with phase A axis
, the dq0 components are d = 0, q = −1, and zero = 0.When you select
90 degrees behind phase A axis
, the default option, the dq0 components are d = 1, q = 0, and zero = 0.
Inputs and Outputs
- αβ0
The vectorized αβ0 signal.
dq0
The vectorized dq0 signal.
wt
The angular position, in radians, of the dq rotating frame relative to the stationary frame.
Example
The power_Transformations
example
shows various uses of blocks performing Clarke and Park transformations.
Version History
Introduced in R2013a